When you flip that switch on the meter from CW to PEP (or AVG to PEP), you're not changing you much power output is coming from the transmitter. You're just changing the method of measurement. I
think most people understand this. They may not understand how the measurements or the math works, but they understand that the transmitter didn't suddenly produce more power. How much power output the transmitter is doing is irrespective of how much of that power is actually present on the fundamental or "intended" frequency. The watt meter doesn't know the difference. This is why "Type accepted" or "certified" (or whatever term you want to use that means the government gave their stamp of approval on them) include other measurements like IMD figures and spurious emissions measurements along with the power output.
My Icom 746pro, 706mkiig, Yaesu 897D, Ameritron AL-811H amp, and Ameritron ALS-500M amp all give their power output ratings in PEP. Does that mean I should call up Icom, Yaesu, and Ameritron and ask them what the output is in "real" watts?
No, of course not. They assume that if I know enough to use the equipment, then I can do the conversion to AVG output if I want to know badly enough. This has nothing to do with trying to sell more stuff; with Amateur equipment they're just using the standard measurement that the FCC requires of Amateur stations. Of course, in the CB world, there are no "standards" for amplifiers and export radios, so people can throw around whatever numbers they want and never have to explain them.
If I want, I can say that the electricity in my house is 155 Volts Peak and it's fed by a 311 Volts Peak mains supply. That doesn't mean my house has any higher voltage than yours - It's still 110V RMS & 220V RMS mains. the 155 peak voltage isn't "fake" voltage; it's just a different way of measuring the same thing.
It's really no different than measuring length or distance. You can say something is 1 foot long, 12 inches, or 30 centimeters. Are any of those measurements fake? Is any measurement better than any other? Does one make you feel better because the number is bigger? As long as you include the measurement method with the figure, everyone should be able to understand what you're talking about, but it doesn't change the physical attributes one bit. I'm not sure how to put it any other way that's clearer.